Chapter 5 Writing Linear Equations - The Standard Form Of A Linear Equation Worksheet - Connie Gross Page 2
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S
H
Writing a Linear Equation
TUDENT
ELP
E X A M P L E 2
Look Back
For help with solving
Write the standard form of an equation of the line passing through (º4, 3) with
linear equations, see
a slope of º2.
p. 155.
S
OLUTION
You are given a point on the line and its slope, so you can write the point-slope
form of the equation of the line.
y º
y
= m(x º
x
)
Write point-slope form.
1
1
y º
= º2[x º (º4)]
3
Substitute for y
, m, and x
.
1
1
y º 3 = º2(x + 4)
Simplify.
y º 3 = º2x º 8
Use distributive property.
2x + y = º5
Add 2x and 3 to each side.
The equation 2x + y = º5 is in standard form.
Horizontal and Vertical Lines
E X A M P L E 3
Write the standard form of an equation
y
a.
of the horizontal line.
(2, 3)
b.
of the vertical line.
1
5
1
1
3
x
S
OLUTION
1
( 3,
1)
a.
The horizontal line has a point with a
y-coordinate of 3. The standard form of
the equation is y = 3.
The vertical line has a point with an
b.
x-coordinate of º3. The standard form
of the equation is x = º3.
. . . . . . . . . .
You have now studied all of the commonly used forms of linear equations. They
are summarized in the following list.
C
ONCEPT
E Q UAT I O N S O F L I N E S
S
UMMARY
y = mx + b
SLOPE-INTERCEPT FORM:
y º y
= m(x º x
)
POINT-SLOPE FORM:
1
1
x = a
VERTICAL LINE (UNDEFINED SLOPE):
y = b
HORIZONTAL LINE (ZERO SLOPE):
Ax + By = C, where A, B, and C
STANDARD FORM:
are real numbers; A and B are not
both zero.
5.6 The Standard Form of a Linear Equation
309
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